2. (Similar to problem 4 in part 2 of Tutorial lab 1) Use MATLAB to plot the direction field of this DE and the solution curve with (0) = 1 mm3. You can take a=1.5 and K=20. Compare it with your sketch in part (b). Screenshot your MATLAB commands and figure and print them out as part of your solution to this assignment.

3. Tumor growth is often modeled by the logistic equation, ac = aC(1 - ), which describes the growth of a cancerous mass (t) over time t. This DE contains two constants: the growth rate of the tumor, a > 0, and the carrying capacity, K > 0. (a) Using any method you like, solve the differential equation above. Your answer will be in terms of constants a and K. (b) If on day t=0 the volume is found to be C(0) = 1 mm3. Sketch the solution curve by finding equilibrium (i.e. critical points) and determining their stability. (c) (Similar to problem 4 in part 2 of Tutorial lab 1) Use MATLAB to plot the direction field of this DE and the solution curve with C(0) = 1 mm3. You can take a=1.5 and K=20. Compare it with your sketch in part (b). Screenshot your MATLAB commands and figure and print them out as part of your solution to this assignment. 3. Tumor growth is often modeled by the logistic equation, ac = aC(1 - ), which describes the growth of a cancerous mass (t) over time t. This DE contains two constants: the growth rate of the tumor, a > 0, and the carrying capacity, K > 0. (a) Using any method you like, solve the differential equation above. Your answer will be in terms of constants a and K. (b) If on day t=0 the volume is found to be C(0) = 1 mm3. Sketch the solution curve by finding equilibrium (i.e. critical points) and determining their stability. (c) (Similar to problem 4 in part 2 of Tutorial lab 1) Use MATLAB to plot the direction field of this DE and the solution curve with C(0) = 1 mm3. You can take a=1.5 and K=20. Compare it with your sketch in part (b). Screenshot your MATLAB commands and figure and print them out as part of your solution to this assignment